Explicit Continuity Conditions for G1 Connection of S-λ Curves and Surfaces
Abstract
:1. Introduction
2. Preliminaries
2.1. Univariate S-λ Basis Functions and S-λ Curve
2.2. Tensor Product S-λ Basis Functions and S-λ Surface
3. Geometric Continuity Conditions for S-λ Curves and Surfaces
3.1. The G1 and C1 Smooth Continuity for S-λ Curves
3.2. The G1 and C1 Smooth Continuity for S-λ Surfaces
4. Numeric Examples
5. Conclusions
- (a)
- (b)
- For any composite S-λ curves and surfaces which satisfy G1 or C1 geometric continuity, its local and global shape can be adjusted flexibly by modifying the shape parameters without changing the control points;
- (c)
- S-λ model can be transformed into different geometric models when the generating functions and transformation factors of the S-λ basis functions are different, so the research of this paper plays an important role in the complex modeling design of other common geometric models as well.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Hu, G.; Li, H.; Abbas, M.; Miura, K.T.; Wei, G. Explicit Continuity Conditions for G1 Connection of S-λ Curves and Surfaces. Mathematics 2020, 8, 1359. https://doi.org/10.3390/math8081359
Hu G, Li H, Abbas M, Miura KT, Wei G. Explicit Continuity Conditions for G1 Connection of S-λ Curves and Surfaces. Mathematics. 2020; 8(8):1359. https://doi.org/10.3390/math8081359
Chicago/Turabian StyleHu, Gang, Huinan Li, Muhammad Abbas, Kenjiro T. Miura, and Guoling Wei. 2020. "Explicit Continuity Conditions for G1 Connection of S-λ Curves and Surfaces" Mathematics 8, no. 8: 1359. https://doi.org/10.3390/math8081359